Ring location

ABSTRACT

The invention concerns a method for locating, in a digital image, a circle centre, comprising the following steps: a) predefining a set of potential radii of the circle; b) dimensioning ( 303 ) two accumulators to a dimension in the form of a column matrix not larger than the size of the image in x-axis and a line matrix not larger than the size of the image in y-axis; c) sequentially, for each pixel of the image: (i) selecting successively each potential radius; (ii) evaluating the position of the potential centre of a circle of the selected radius and whereof the pixel concerned is on the periphery; and (iii) incrementing said accumulators at the x-axis and the y-axis of the potential centre; and d) selecting ( 304 ), as coordinates of the located centre, the x-axis and the y-axis corresponding to the maximum of accumulators.

[0001] The present invention relates to the localization, in a digitizedimage, of a ring-shaped surface included between two substantiallyconcentric geometric shapes of generally circular shape. Morespecifically, the present invention relates to the detecting of a ringextending between two circles of different radiuses, the circle havingthe smaller radius being strictly included in the circle of greaterradius.

[0002] An example of application of the present invention is thelocalization of the iris of an eye in a digitized image. Indeed, an eyemay be characterized as being an assembly of substantially concentricelliptic geometric shapes: the eyebrows define a contour that isfollowed by eyelashes, which surround the eye ground, which includes asubstantially circular iris containing a substantially circular pupil.In such an approximately concentric pattern, the position of the centersand radiuses of the two circular patterns of the pupil and of the irisis desired to be extracted, to extract from the image the ring formingthe iris. For clarity, it is considered in the following descriptionthat the limits of the pupil and of the iris are perfect circles.

[0003]FIG. 1 illustrates, in a flowchart, an example of a known methodfor localizing an iris of an eye. FIGS. 2A to 2C illustrate the digitalimage which is the object of the method at different steps of theimplementation thereof.

[0004] Such a method starts with a step 101 (ACQUIRING EYE IMAGE) inwhich a digital image of an eye is acquired. The eye is digitized sothat the obtained image is full size (scale 1:1). Such an image may beobtained by any biometry terminal enabling capturing an eye image. Forexample, the acquisition is performed by a CCD digital camera of a580×760-pixel image, in black and white by infrared illumination, theeye being placed at a few centimeters only of the camera.

[0005] Localizing an iris in such an image then consists of localizingthe center and the radius of the pupil as well as the center and theradius of the iris. Indeed, although the pupil is strictly included inthe iris, its is generally slightly off-centered with respect thereto.

[0006] A known method for determining the centers of the pupil and ofthe iris and their radiuses is based on the following observation. Ininfrared illumination, on the one hand, the iris contrasts on the whiteof the eye. On the other hand, the contour of the pupil contrasts withrespect to the peripheral iris. This contrast translates on the digitalimage as very different levels of grey on either side of the limitbetween the iris and the cornea, on the one hand, and of the limitbetween the iris and the pupil, on the other hand. The gradient, interms of levels of grey, of the points located on the iris or pupilcontour is then very high. Generally, the contrast between the pupil andthe iris is greater than the contrast between the iris and the cornea.

[0007] Localizing the iris consists of successively considering eachpoint in the image as the possible center and of measuring the gradientsof the points located on arcs of a circle centered on the consideredpossible center. The radiuses of these arcs of a circle vary within arange of possible radiuses of a pupil or of an iris at the considereddigitization scale. For a 580×760-pixel image at scale 1:1, the pupildiameter is considered to range between 30 and 100 pixels, and the irisdiameter is considered to range between 100 and 180 pixels. The centerof the pupil or of the iris then is the point for which, in the radiusrange corresponding to the pupil, respectively, to the iris, thegradient variation is the most significant. The gradient variationcalculations are performed by means of integro-differential operators.

[0008] To reduce the amount of calculation and the processing time, theintegro-differential operators are applied, at step 102 (LOCATING IRIS)which follows acquisition 101, to successive grids of pointsrepresenting possible centers. The successive grids have decreasingdimensions and pitches. Thus, in a first iteration 103 (i=0, s=s₀), itis for example chosen to apply on the digitized image illustrated inFIG. 2A a first grid of dimensions close to those of the image and of arelatively large first pitch s₀, for example, s₀=25 pixels, that is,including a possible center every 25 pixels in both directions. Further,the centers of the iris and of the pupil being confounded or slightlyoff-centered, the center and contour of the sole pupil are firstlocalized by applying the operators on arcs of a circle having diametersvarying from 30 to 100 pixels.

[0009] At the next iteration i=1, the grid pitch is reduced to refinethe center determination. This pitch reduction goes along with areduction of the grid dimensions and a centering thereof in the regionof highest gradient variations. As illustrated in FIG. 2B, it isconsidered, for example, that for second iteration i=1, pitch s₁ is 10pixels. If the number of points in the grid is constant, its sizereduction is automatic with the pitch reduction.

[0010] Again, the integro-differential operators are applied for eachpoint in the grid and the existence of a center or of a region in which,for several points, the gradient variation (levels of grey) is thestrongest is detected.

[0011] For each iteration i and each corresponding pitch s_(i), theprocess is thus repeated by applying in a block 104(INTEGRO-DIFFERENTIAL OPERATOR) the integro-differential operators ongrids of decreasing pitch s_(i) and of more and more reduced dimensions.

[0012] After each passing through block 104, a possible center andradius are obtained for the pupil at block 105 (CENTER & RADIUS), whichare included in the grid of smaller pitch at the next iteration.

[0013] It is controlled at the following step 106 (i=V? s_(i)=SV?)whether a precision criterion is achieved. This criterion is defined bya number V of iterations or a pitch S_(v) of the grid for which theobtained center and radius are considered as being localized in asufficiently accurate manner.

[0014] If not (N), a new grid of reduced dimensions and of smallerpitch, centered on the region for which the strongest gradient variationhas been observed at the preceding iteration is redefined at step 107(NEW GRID, i=i+1, s_(i)=s_(i+1)).

[0015] Generally, the process carries on until a maximum accuracy, thatis, a grid having a pitch of one pixel, is reached, as illustrated inFIG. 2C. Such an accuracy enables exact determination of center C_(P)and radius R_(P) of the pupil.

[0016] Once precision test 106 is positive (Y), the iris is localized atthe next step 108 (IRIS) by applying again a grid of possible centers todetermine with the integro-differential operators the iris radius R_(I)and, should the case arise, discriminate its center C_(I) from centerC_(P) of the pupil with a maximum reliability. The operators are hereapplied on arcs of a circle having diameters ranging from 100 to 180.Since the circles are approximately concentric, it is not necessary tostart again from a grid having the maximum pitch. A reduced number ofiterations (or even a single iteration) may be used by centering on thecenter of the pupil a grid sized according to the maximum(physiologically) possible interval between the two centers. Such acenter localization and radius determination of a second circle afterlocalizing a first circle is described in U.S. Pat. No. 5,291,560.

[0017] The iris surface, that is, the ring-shaped surface between thepupillary circle of center C_(P) and of radius R_(P) and the iridiancircle of center C_(I) and of radius R_(I), is then determined with amaximum accuracy.

[0018] The surface thus obtained may be submitted to any appropriatedigital processing. In the considered example of an iris, it generallyis an iridian recognition method based on the matching 109 (MATCHING) offeatures extracted from the obtained surface, for example, in one of theways described in above-mentioned U.S. Pat. No. 5,291,560 or inabove-mentioned U.S. Pat. No. 5,572,596, or in international patentapplication WO 00/62239.

[0019] Generally, the method described in relation with FIGS. 1 and 2enables localizing at least one circle by exact determination of itsradius and of the position of its center.

[0020] A major disadvantage of such a method is the successiverepetition of the same operations on grids of decreasing size and pitch.This imposes a great amount of calculation. Further, for a given point,for example, point A of FIG. 2A close to the searched centers, thecalculations are repeated a great number of times. Accordingly, such amethod has a slow implementation.

[0021] Further, the various gradient variation comparison operations andthe corresponding calculations impose a relatively complex and bulkysoftware structure. Further, at each iteration, for each possiblecenter, the obtained data must be stored to be compared to thoseobtained for the other possible centers, to determine the region(s) ofstrongest gradient variation. This is necessary to recenter the nextgrid at step 107. Such a method thus requires using a significant memorysurface.

[0022] In a completely different field, to recognize the presence of aface in a digitized image, a method for determining the presence of acornea or of an iris has been provided to identify the presence of aneye and calculate a spacing between two eyes. This method consists ofsearching concentric geometric shapes by means of a Hough transform suchas described in U.S. Pat. No. 3,069,654. Such a method consists ofconsidering, for the involved geometric shape (here, a circle), eachpixel of the digitized image as being at the periphery of a circle of agiven perimeter (radius), and of approximately localizing the center ofthis circle. For each possible diameter of the searched circuit, anaccumulator of same dimensions as the image is associated with thedigitized image. Each accumulator memorizes, for a given radius, thenumber of times when a given point of the digitized image is determinedas being the possible center of the searched circle. This is performedby incrementing, for each radius, an initially null weight assigned, inthe accumulator linked to this radius, to the position of the possiblecenter in the image.

[0023] The searched center and radius are then obtained by determining,for each considered radius, the point having the greatest weight and,for the different considered radiuses, that for which the possiblecenter has the maximum weight with respect to the other possible centersdetermined by the first determination. Such a method is described, forexample, in article “Detection of eye locations in unconstrained visualimages” by R. Kothari and J. L. Mitchell, published in Proc. ICIP '96,III pp. 519-523 (1996), or in article “Eye spacing measurement forfacial recognition” by M. Nixon, published in SPIE Proc., 575, pp.279-285 (1985).

[0024] Such a method has the disadvantage of being also long to execute.Further, for each pixel in the image, it imposes using a bulky memory,since, for each possible radius, an array having a number of lines andcolumns equal to the number of lines and columns of the digitized imagemust be memorized.

[0025] The present invention aims at providing a method for accuratelylocating the center of at least two concentric circles, which is fasterthan known methods.

[0026] The present invention also aims at providing such a method ofwhich the implementation requires a reduced memory space as compared tothe space required by the implementation of known methods.

[0027] The present invention also aims at providing such a method whichalso applies to the localization of several circles, each of which isstrictly included in a circle of larger radius, but which are notconcentric.

[0028] The present invention also aims at providing a method forlocalizing a ring included between two circles.

[0029] The present invention also aims at providing such a method whichis applicable to the localization of an iris of an eye in a digitizedimage.

[0030] To achieve these and other objects, the present inventionprovides a method for localizing, in a digital image, at least twocircles, one of which is strictly included in the other by determinationof their radiuses and of the coordinates of their centers by means ofintegro-differential operators applied to at least one grid of possiblecenters, including the steps of:

[0031] evaluating an approximate position of the center of one of thetwo circles; and

[0032] centering the grid in the vicinity of the approximate center, thegrid being of reduced dimensions as compared to the image dimensions.

[0033] According to an embodiment of the present invention, the methoduses a single grid having a minimum pitch.

[0034] According to an embodiment of the present invention, the maximumsize of the grid is smaller than the size of the larger circle.

[0035] According to an embodiment of the present invention, the maximumsize of the grid is smaller than the size of that of the circles formingthe limit of strongest contrast.

[0036] According to an embodiment of the present invention, the maximumsize of the grid is smaller than the size of the smaller circle.

[0037] According to an embodiment of the present invention, the step ofevaluation of the approximate position of the center includes the stepsof:

[0038] a) predefining a set of possible radiuses of the circle;

[0039] b) sizing two one-dimension accumulators in the form of a columnarray of at most the image size in abscissa and of a line array of atmost the image size in ordinate;

[0040] c) successively, for each image pixel:

[0041] i) successively selecting each possible radius;

[0042] ii) evaluating the position of the possible center of a circle ofthe selected radius and the considered pixel of which is on theperiphery; and

[0043] iii) incrementing the accumulators at the abscissa and ordinateof the possible center; and

[0044] d) selecting, as coordinates of the located center, the abscissaand the ordinate corresponding to the maximum of the accumulators.

[0045] According to an embodiment of the present invention, theincrement is one.

[0046] According to an embodiment of the present invention, theincrement is weighted according to the significance of the gradient atthe considered pixel.

[0047] The present invention also provides a method for localizing, in adigital image, a ring defined by the inclusion of a first circle ofrelatively small radius in a second circle of relatively large radius,consisting of localizing the first and second circles according to themethod of any of the preceding embodiments.

[0048] According to an embodiment of the present invention, the ring isthe iris of an eye, the first circle being the pupil of the eye and thesecond circle being the limit between the iris and the eye cornea.

[0049] According to an embodiment of the present invention, the pupil isthat of the circles of which the center is approximately searched.

[0050] The foregoing objects, features and advantages of the presentinvention, will be discussed in detail in the following non-limitingdescription of specific embodiments in connection with the accompanyingdrawings, in which:

[0051]FIG. 1 illustrates in a flowchart the step sequence of a knowniridian recognition method;

[0052]FIGS. 2A to 2C schematically and partially illustrate theimplementation of the method of FIG. 1;

[0053]FIG. 3 illustrates in a flowchart the step sequence of an iridianrecognition method according to an embodiment of the present invention;and

[0054]FIGS. 4A to 4D illustrate the implementation of the method of FIG.3.

[0055] For clarity, the same elements have been designated with samereferences in the different drawings. Further, FIGS. 2A to 2C and 4A to4D are not drawn to scale.

[0056] A mode of iris recognition and location by determining thepupillary and iridian radiuses and by localizing the centers of thepupil and of an iris of an eye according to the present invention isdescribed hereafter in relation with FIGS. 3 and 4A to 4D.

[0057] The method starts with a step 301 (ACQUIRING EYE IMAGE) ofacquisition of an eye image. Preferably, such an acquisition isperformed so that the obtained image exhibits dimensions very close tothe model, that is, a scale as close to one as possible. Such anacquisition may be performed by means of an appropriate conventionalbiometry terminal, for example, the device described in documentEP-A-0,973,122.

[0058]FIG. 4A illustrates an image of an eye obtained by acquisition 301by a digital CCD camera having a 580×760-pixel image, the eye beingplaced at a few centimeters only of the camera and being submitted to aninfrared illumination. The obtained image includes a pupil P, an iris I,a cornea limited by a higher eyelid HE and a lower eyelid LE.

[0059] The method according to the present invention carries on with theapproximate localization of the eye center, that is, of the center ofthe pupil or of the iris. Preferably, the center of the circleexhibiting the strongest contrast is approximately located. As indicatedpreviously, in infrared illumination, the contrast is generally higherbetween the pupil and the iris than between the iris and the cornea.Preferably, the center of the pupil is thus first approximately located.The approximate localization enables determining an approximate centerwhich is, with respect to the real searched center, at a distance of atmost five pixels.

[0060] According to a first embodiment of the present invention, notshown, the approximate center is determined by means of any knownmethod. For example, one can use the method disclosed in the article “Anew memory model for the parameter space in the Hough transform:Projection arrays” of M. H. Kim and H. Y. Hwang published in ProceedingsTENCON 87, IEEE region 10 conference “Computers and CommunicationsTechnology Toward 2000”, Aug. 25-28, 1987, Volume 1, pages 222-226.

[0061] According to a preferred embodiment of the present invention, theapproximate center is determined by means of a method, an algorithm ofwhich is described hereafter in relation with FIG. 3.

[0062] As illustrated in block 302 (LOCATING IRIS) of FIG. 3, twoone-dimensional accumulators W_(x) and W_(y) are first generated. Thedimension of a first accumulator W_(x) is number N of lines of the imagebeing processed. The dimension of the second accumulator WY is number Mof image columns. In a first sub-step 303, all current elements of thefirst and second accumulators W_(x)(i) where i varies from 1 to N, andW_(y)(j), where j varies from 1 to M, are set to zero.

[0063] The system is initialized to be placed at the first line (block304, x=1), on the first column (block 305, y=1) and consider a first(block 306, k=1) possible radius.

[0064] The localization is performed by successively implementing foreach of the N lines x, for each point P_(xy) at the intersection ofcurrent line x and of a column y among the M columns, the followingoperations (block 307):

[0065] calculating components Grad, and Grady of the gradient of currentpoint Pxy, that is, comparing the level of grey of the current pixelwith the levels of grey of the neighboring points;

[0066] calculating abscissa x_(c) and ordinate y_(c) of center C of thecircle crossing current point P_(xy), to which the gradient determinedat the preceding step is tangent. Coordinates x_(c) and y_(c) can bededuced, from components Grad, and Grady of the gradient and theequation of the circle of center C of radius R_(k), as follows:${{x_{c}\left( {x,R_{k}} \right)} = {x \pm \frac{R_{k}}{\sqrt{1 + \frac{{Grad}^{2}y}{{Grad}^{2}x}}}}};{{{and}\quad {y_{c}\left( {y,R_{k}} \right)}} = {y \pm {\frac{R_{k}}{\sqrt{1 + \frac{{Grad}^{2}x}{{Grad}^{2}y}}}.}}}$

[0067] The considered radius R_(k) is sampled from a set of K possibleradiuses of the previously defined circle.

[0068] incrementing by one unit the first accumulator at positionW_(x)(i) corresponding to abscissa x_(c) of center C thus calculated;and incrementing by one unit the second accumulator at position W_(y)(j)corresponding to ordinate y_(c) of center C thus calculated. As analternative, the increment may be an amount weighted according to thesignificance of the gradient at the current point P_(xy) for which pointC is the center of the circle of radius R_(k) to which this gradient istangent.

[0069] The successive operations of calculation of coordinates x_(c) andy_(c) are performed for each point P_(xy) for each of the K possiblevalues of radius R_(k), for example, for a pupil between 30 and 100pixels.

[0070] For a considered point P_(xy), the only values to be stored arethose of components Grad_(x) and Grad_(y) of the gradient and thecontent of the two accumulators W_(x) and W_(y). The two coordinatesx_(c) and y_(c) of center C, recalculated for each radius R_(k), neednot be stored.

[0071] It is then successively controlled:

[0072] whether, for current point P_(xy), all K radiuses have beenprocessed (step 308, k=K?);

[0073] whether, for the considered line x, the M columns (or pixels)have been scanned (step 309, y=M?); and

[0074] whether the last line N has been reached (step 310, x=N?).

[0075] As long as one of the preceding conditions 308, 309, 310 is notfulfilled (N), the corresponding counter of radius k is incremented(block 311, k=k+1), as well as the counter of column y (block 312,y=y+1) or of line x (block 313, x=x+1) and the appropriate sequence isresumed by returning either to the processing of the next radius byblock 307, or to the processing of the point of the next column, fromblock 306, or to the processing of the next line, from block 305.

[0076] As the calculations advance, the two components Grad_(x) andGrad_(y) of the gradient are recalculated for each current point P_(xy).When passing to a next point, the values associated with the precedingpoint are no longer necessary.

[0077] Thus, the same memory space can be used to store this parameternecessary to the K calculations of as many possible centers according toradiuses R_(k). The same minimum memory space can thus be assigned tothese buffer calculations for each change of current point. From onepoint to another, the only data to be kept are the contents of the twoaccumulators W_(x) and W_(y),

[0078] As illustrated in block 314, abscissa X0 of the approximatesearched center C0 is the value for which the corresponding termW_(x)(X0) of the first accumulator W_(x) is maximum. Similarly, ordinateY0 of point C0 is the point for which value W_(y)(j) is maximum:

[0079] W_(x)(X0)=Max(i=1 . . . N)[W_(x)(i)], and

[0080] W_(y)(Y0)=Max=(j=1 . . . M)[W_(y)(j)].

[0081] Coordinates XO and Y0 of center C0 are accordingly obtained bydetermining, in each accumulator W_(x) and W_(y) the respective currentpositions i and j for which the respective values W_(x)(i) and W_(y)(j)are maximum.

[0082]FIG. 4B illustrates the result obtained at the end of step 314.

[0083] At the next step 315 (INTEGRO-DIFFERENTIAL OPERATORS AROUND (X0,Y0)), steps of searching the center and the radius of a circle areimplemented based on integro-differential operators applied on a gate Gof points representing possible centers. The searched circle is that ofthe pupil. As illustrated in FIG. 4C, grid G is, according to thepresent invention, of fine pitch (preferably, a minimum pitch, that is,I pixel) and is centered on previously-determined approximate center C0.This amounts to implementing steps 104 and 105 of the method of FIG. 1,but directly for final determination grid G. As an alternative, theexecution of a few loops of the method of FIG. 1 according to theapproximate center determination accuracy may be maintained. Grid Gbeing already centered on approximate center C0, the determination ofthe exact center C_(P) and radius R_(P) of the pupil is particularlyfast. Indeed, even if it is chosen to perform several runs, the numberof successive grids, and thus the amount of calculation, is reduced ascompared to the known method such as previously described. It should benoted that this exact determination of center Cp and of radius Rp of thepupil uses the same set of K possible values for the pupil radius asthat previously defined and used to determine approximate center C0.

[0084] Once center C_(P) and radius R_(P) of the pupil have beendetermined, integro-differential operators are applied again on circleshaving their radiuses in a possible range of the average diameter of theiris of an eye to determine (block 316 (IRIS CENTER & BOUNDARIES) ofFIG. 3; FIG. 4D) radius R_(I) and center C_(I) of the iris. As for thepupil, this determination preferentially uses a single grid with aminimum pitch. This grid is centered on center C_(P) and its dimensionsare a function of the maximum possible distance between centers C_(P)and C_(I), so that it necessarily includes center C_(I).

[0085] The ring forming the eye iris has thus been precisely located. Itcan then be submitted to any appropriate processing, for example, arecognition processing by being compared to the content of a database(block 317, MATCHING).

[0086] The general time of localization of the ring forming the iris isconsiderably reduced as compared to conventional methods implementingfor the entire image a series of successive grids of possible centers ofdecreasing dimensions and pitches. Further, the precision of thislocalization is maximum.

[0087] The iris localization method described in relation with FIGS. 3and 4 generally enables locating by determination of its center and ofits radiuses any elliptic geometric shape. In the very example of thelocating of an iris, instead of considering the pupil and/or the iris asa perfect circle, these may be considered as having an elliptic shape,either upon determination of the approximate center—steps 303 to 314 ofFIG. 3—or upon application 315 of the integro-differential operatorswhich are then applied on arcs of an ellipse instead of on arcs of acircle.

[0088] Generally, the method according to the present invention appliesto the locating by determination of their centers and radiuses of anynumber of elliptic geometric shapes, each geometric shape being strictlyincluded in a geometric shape of greater perimeter, except for thathaving the greatest dimensions. Further, the searched elliptic shapesare concentric or slightly off-centered.

[0089] This localization method may be used to locate at least one ringincluded between at least two of the located geometric shapes. Forexample, in the wood working industry, it enables detecting the presenceof knots in the wood in quality control tests. It is then alsoadvantageously possible to measure their size, which enables determiningtheir impact on the solidity of the final product.

[0090] In the previously-described iris localization application, thelocalization is previous to an iridian recognition usable as arecognition parameter to identify an individual. An example ofapplication is the access control: access to a physical site, such as acontrol of the opening of a door with a code, or with an access card;access to a bank account usually protected with a password; access toany device such as a computer or a mobile phone usually protected by acode to be typed. Such a device may also replace the fingerprintidentification or another biometric identification.

[0091] Of course, the present invention is likely to have variousalterations, modifications, and improvement which will readily occur tothose skilled in the art. In particular, it has been considered in FIG.4 that the method starts with the acquisition of an eye image. However,it may start with the access in a database to a previously-digitizedimage. This image may then come from a distant database. In FIG. 4C, ithas been assumed that center C_(P) differs from approximate center C0.However, approximate center C0 could appear to be the searched center ofthe pupil. In the approximate center search algorithm, the image hasbeen assumed to be scanned line by line. It should be clear to thoseskilled in the art that any other type of scanning, for example, columnby column, would also be possible. Further, the loop control mode (linecounter x, column counter y, radius counter k) may be modified in anyappropriate manner. Moreover, instead of searching the center of thepupil as the approximate center, that of the iris could be searched,provided to appropriately modify the predefined set of possible valuesfor the radius.

[0092] Further, the circle forming the limit with the strongestcontrast, that is, that having the points with the highest gradientvalues, has approximately been located among searched circles of variouspossible radiuses. It would however be possible to attempt to determinethe approximate center of another circle of lower contrast, for example,if said circle has a particularly reduced number of possible radiuses.

1. A method for localizing, in a digital image, at least two circles oneof which is strictly included in the other, by determination of theirradiuses and of the coordinates of their centers by means ofintegro-differential operators applied to at least one grid of possiblecenters, characterized in that it includes the steps of: evaluating anapproximate position of the center of one of the two circles; andcentering the grid in the vicinity of the approximate center, the gridbeing of reduced dimensions as compared to the image dimensions.
 2. Themethod of claim 1, using a single grid having a minimum pitch.
 3. Themethod of claim 2, wherein the maximum size of the grid is smaller thanthe size of the larger circle.
 4. The method of claim 3, wherein themaximum size of the grid is smaller than the size of that of the circlesforming the limit of strongest contrast.
 5. The method of claim 3,wherein the maximum size of the grid is smaller than the size of thesmaller circle.
 6. The method of claim 1, wherein the step of evaluationof the approximate position of the center includes the steps of: a)predefining a set of possible radiuses of the circle; b) sizing twoone-dimension accumulators in the form of a column array of at most theimage size in abscissa and of a line array of at most the image size inordinate; c) successively, for each image pixel: (i) successivelyselecting each possible radius; (ii) evaluating the position of thepossible center of a circle of the selected radius and the consideredpixel of which is on the periphery; and (iii) incrementing theaccumulators at the abscissa and ordinate of the possible center; and d)selecting, as coordinates of the located center, the abscissa and theordinate corresponding to the maximum of the accumulators.
 7. The methodof claim 6, wherein the increment is one.
 8. The method of claim 6,wherein the increment is weighted according to the significance of thegradient at the considered pixel.
 9. A method for localizing, in adigital image, a ring defined by the inclusion of a first circle ofrelatively small radius in a second circle of relatively large radius,consisting of localizing the first and second circles according to themethod of claim
 1. 10. The method of claim 9, wherein the ring is theiris of an eye, the first center being the pupil of the eye and thesecond circle being the limit between the iris and the eye cornea. 11.The method of claim 10, wherein the pupil (P) is that of the circles ofwhich the center is approximately searched according to the method ofclaim 1.